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Zbl 1008.43009
Kobayashi, Toshiyuki
Branching problems of unitary representations. (English)
[A] Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. II: Invited lectures. Beijing: Higher Education Press. 615-627 (2002). ISBN 7-04-008690-5/3-vol. set

Basic theory and new perspectives of admissible restrictions are presented from both the analytic and the algebraic point of view, such as:\par 1. Admissible restrictions to subgroups, including a criterion for admissible restrictions and its converse statement;\par 2. infinitesimal discrete decomposability, including a discrete branching law, a criterion for discrete decomposability and the size of irreducible summands;\par 3. some applications to representation theory;\par 4. new discrete series for homogeneous spaces, nonsymmetric spaces, symmetric spaces and an exclusive law of discrete spectrum for restriction and induction;\par 5. modular varieties and vanishing theorems, including vanishing theorems for modular symbols.
[Su Weiyi (Nanjing)]

MSC 2000:: *43A85 Analysis on homogeneous spaces
22E46 Semi-simple Lie groups and their representations
11F67 Special values of automorphic L-series, etc
53C50 Lorentz manifolds, manifolds with indefinite metrics
53D20 Momentum maps; symplectic reduction

Keywords: admissible restrictions; infinitesimal discrete decomposability; discrete branching law; discrete series; modular varieties; vanishing theorems

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